Problem: Solve for $x$ : $4x^2 + 32x - 80 = 0$
Answer: Dividing both sides by $4$ gives: $ x^2 + {8}x {-20} = 0 $ The coefficient on the $x$ term is $8$ and the constant term is $-20$ , so we need to find two numbers that add up to $8$ and multiply to $-20$ The two numbers $-2$ and $10$ satisfy both conditions: $ {-2} + {10} = {8} $ $ {-2} \times {10} = {-20} $ $(x {-2}) (x + {10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -2) (x + 10) = 0$ $x - 2 = 0$ or $x + 10 = 0$ Thus, $x = 2$ and $x = -10$ are the solutions.